We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto-optimal solutions among a finite set of candidates for which the objective function values have to be estimated from noisy evaluations. When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal may appear to be dominated, and solutions that are truly dominated may appear to be Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objectives, and exploits this information to decide how to resample. The experiments are designed to evaluate the algorithm on several artificial and practical test problems. The proposed approach is observed to consistently outperform its competitors (a well-known state-of-the-art algorithm and the standard equal allocation method), which may also benefit from the use of stochastic kriging information.

中文翻译：

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使用随机克里金法进行双目标排序和选择


我们考虑双目标排序和选择问题，其目标是在一组有限的候选者中正确识别帕累托最优解，其目标函数值必须从嘈杂的评估中估计。在识别这些解时，扰乱观察到的性能的噪声可能会导致两种类型的误差：真正 Pareto-optimal 的解可能看起来占主导地位，而真正占主导地位的解可能看起来是 Pareto-最优的解。我们提出了一种新的贝叶斯双目标排序和选择方法，该方法按顺序将额外的样本分配给竞争解决方案，以减少在识别具有最佳预期性能的解决方案时的错误分类误差。该方法使用随机克里金法来构建目标的可靠预测分布，并利用此信息来决定如何重采样。这些实验旨在评估算法在几个人工和实际测试问题上的表现。据观察，所提出的方法始终优于其竞争对手（一种众所周知的最先进的算法和标准的相等分配方法），后者也可能受益于随机克里金信息的使用。